Punctured convolutional codes have been widely used for many years. A punctured convolutional code is a convolutional code in which selected bits are removed, or “punctured”, to increase the data rate. For example, a rate 1/2 convolutional code produces two coded bits for every one data bit. If this code is punctured by removing one out of every 4 coded bits, the resulting code rate is 2/3. Such codes are useful because the same encoder and decoder can be used for different code rates.
A punctured convolutional code is uniquely defined by its generator polynomial and a “puncturing” or “perforation” pattern. The generator polynomial defines the relationship between the input bits and the coded bits (before puncturing). The puncturing pattern specifies the pattern in which coded bits are removed. Finding the optimal puncturing pattern can be a difficult task, especially for coding rates in which the number of possibilities is large. Optimal codes have been found for a large number of data rates. However, optimal codes for other data rates remain undiscovered. Optimal codes permit operation at a lower signal-to-noise ratio (SNR) for a given data arte and bit-error probability.
The current Multiband OFDM Alliance (MBOA) proposal uses a generator polynomial of G=[133 145 175]8. The MBOA proposal specifies four puncturing patterns for code rates of R=11/32, 1/2, 5/8, and 3/4, using quadrature phase shift keying (QPSK). Additional modes with code rates R=1/3 and R=3/8 are also being considered. An alternate code using a generator polynomial G=[133 145 175]8 and new puncturing patterns with better properties that the MBOA proposal has been suggested for code rates R=5/8 and R=3/4. A description of how the bits are encoded and punctured may be found in the Multiband OFDM Alliance (MBOA) draft specification for Ultra-Wide-Band (UWB) communications. The details of the draft specification for the IEEE 802.15.3a standard may be found in the document “Multi-band OFDM Physical Layer Proposal for IEEE 802.15 Task Group 3a”, document IEEE P802.15-03/268r0, dated Jul. 21, 2003, by the Institute of Electrical and Electronics Engineers, Inc., which draft specification is hereby incorporated herein by reference, in its entirety.
The Multi-band OFDM Physical Layer Proposal for IEEE 802.15 Task Group 3a, dated Jul. 21, 2003 specifies a convolutional code and perforation patterns for a number of different code rates. For example, code rates of 1/3, 11/32, 1/2, and 3/4 are provided using a generator polynomial for an original 1/3 rate code, and designated perforation patterns. The performance of the original convolutional codes as proposed in the MBOA draft specification has been found to be sub-optimal.
Further limitations and disadvantages of conventional and traditional approaches will become apparent to one of ordinary skill in the art through comparison of such systems with the present invention as set forth in the remainder of the present application with reference to the drawings.